CANTON - Count on Cantor

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One of the famous proofs of modern mathematics is Georg Cantor's demonstration that the set of rational numbers is enumerable. The proof works by using an explicit enumeration of rational numbers as shown in the diagram below.

1/1 1/2 1/3 1/4 1/5 ...
2/1 2/2 2/3 2/4
3/1 3/2 3/3
4/1 4/2
5/1

In the above diagram, the first term is 1/1, the second term is 1/2, the third term is 2/1, the fourth term is 3/1, the fifth term is 2/2, and so on.

Input

The input starts with a line containing a single integer t <= 20, the number of test cases. t test cases follow.

Then, it contains a single number per line.

Output

You are to write a program that will read a list of numbers in the range from 1 to 10^7 and will print for each number the corresponding term in Cantor's enumeration as given below.

Example

Input:
3
3
14
7

Output:
TERM 3 IS 2/1
TERM 14 IS 2/4
TERM 7 IS 1/4

hide comments
codesok: 2016-12-03 14:41:04

TAKE PEN AND PAPER, DRAW AND OBSERVE CAREFULLY

esshuvo: 2016-11-01 17:43:46

Not only have to do "find out" what is said in the problem but also while implementing this problem is helpfull for the novice like me!

parthendo: 2016-10-06 21:32:26

Read CAREFULLY and it's AC ;)

vdbhatt: 2016-09-20 22:41:43

good problem... use pen-paper

jawad_cs: 2016-09-12 02:07:26

Please help me...it is mentioned in the question that the 4th term is 3/1.....is it correct...i think it should be 1/3..it would form a pattern then

rajat_bir2015: 2016-08-30 22:38:35

plot the graph to get the pattern

nikunjsoni: 2016-08-17 16:53:09

AC in first attemp :) time - 0.00

sharif ullah: 2016-08-11 21:22:32

here number of test case is 20 .so pre-calculation may give TLE

SidXDDD: 2016-07-16 17:48:38

Last edit: 2016-07-20 16:02:11
Pikachu: 2016-07-13 16:52:09

Last edit: 2016-07-13 16:56:04

Added by:Thanh-Vy Hua
Date:2005-02-27
Time limit:5s
Source limit:50000B
Memory limit:1536MB
Cluster: Cube (Intel G860)
Languages:All except: NODEJS PERL 6 VB.net
Resource: ACM South Eastern European Region 2004